code: def test_active_dims(self):
      x1 = torch.tensor(
          [[4, 2], [3, 1], [8, 5], [7, 6]], dtype=torch.float
      )
      x2 = torch.tensor([[4, 2], [3, 0], [4, 4]], dtype=torch.float)
      lengthscale = 2
      kernel = CategoricalKernel(active_dims=[0]).initialize(
          lengthscale=lengthscale
      )
      kernel.eval()
      dists = x1[:, :1].unsqueeze(-2) != x2[:, :1].unsqueeze(-3)
      sc_dists = dists / lengthscale
      actual = torch.exp(-sc_dists.mean(-1))
      res = kernel(x1, x2).to_dense()
      self.assertAllClose(res, actual)
  
file_path: botorch/test/models/kernels/test_categorical.py
imports: import torch
  from botorch.models.kernels.categorical import CategoricalKernel
  from botorch.utils.testing import BotorchTestCase
  from gpytorch.test.base_kernel_test_case import BaseKernelTestCase
label_desc: Use image node_id 8 for calling the TestCategoricalKernel obj's underlying member method code with example usage: obj.test_active_dims() without return types